In this paper, we propose a new analytical method called generalized Taylor fractional series method (GTFSM) for solving nonlinear timefractional reaction-diffusion-convection initial value problems. Our obtained results are given in the form of a new theorem. The advantage of the proposed method compared with the existing methods is, that method solves the nonlinear problems without using linearization and any other restriction. The accuracy and efficiency of the method is tested by means of two numerical examples. Obtained results interpret that the proposed method is very effective and simple for solving different types of nonlinear fractional problems.